- #1
trap101
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Sketch the graph of the equation x - e^(1-x) - y^3 = 0, Show that for each x there is a unique y satisfying the equation.
Attempt:
So the first thing I did was isolate y in order to put the equation in a form to graph (somewhat). did that and got y = (x-e^(1-x))^1/3.
Got the y-int: (0, -e^1/3), x-int: (1,0) [I didn't get this, this was in soln, how'd they get?]
Now after my attempt to graph it, I look at the solution and they say:
we see that the graph is asymptotic to the curve y= x^1/3 as x-->∞ and asymptotic to the curve y = -e^[(1-3)/3] as x --> -∞
How is there any asymptotic behavior? The expression doesn't indicate any restrictions. This is based on Implicit Function Thm by the way
Attempt:
So the first thing I did was isolate y in order to put the equation in a form to graph (somewhat). did that and got y = (x-e^(1-x))^1/3.
Got the y-int: (0, -e^1/3), x-int: (1,0) [I didn't get this, this was in soln, how'd they get?]
Now after my attempt to graph it, I look at the solution and they say:
we see that the graph is asymptotic to the curve y= x^1/3 as x-->∞ and asymptotic to the curve y = -e^[(1-3)/3] as x --> -∞
How is there any asymptotic behavior? The expression doesn't indicate any restrictions. This is based on Implicit Function Thm by the way